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Each element of m is the greatest subscript such that b = A(m).
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A can be a cell array of strings.Īlso returns index vectors m and n such that b = A(m) and A = b(n). The resulting vector is sorted in ascending order. Returns the same values as in A but with no repetitions. Let’s do some validation of our code.Unique (MATLAB Functions) MATLAB Function Reference Otherwise, if it is 0, we will find the line segment where overlapping occurs. If the line segments are collinear/parallel and q_p_cross_r is not 0, then there is no intersection. Now, let’s check if the two line segments are collinear or parallel. Then, as described by Gareth Rees, we can solve for the intersection using the following two equations: % t = (q-p) x s/(r x s) % Solve for all of these variables given the two line segments % Check if two line segments (A and B) intersect in 2D space.Īs we described previously, we will utilize parametric equations for the two line segments, such that segment1 = p + t*r and segment2 = q + u*s, where t and u range from 0 to 1. function = checkSegmentIntersection(A, B) We will therefore only check for the first and fourth possibilities. Our default initialization of “false” and NaN will be the outputs for the second, third and fifth possibilities. The output arguments of “doesIntersect” will be a boolean value true/false and “intersection” will provide the intersection point (or line segment) if there is an intersection (or overlap). These input arguments will be 2×2 arrays with each row describing the endpoints of the line segment.
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Now let’s define our function “checkSegmentIntersection”, which will take as input two line segments (A and B). We can therefore either append a 0 to all of our 2-D line segments or use the following function, which returns only the k vector (ignoring the i and j vectors) of the cross product. With math, graphics, and programming, it's designed for the way you think and the work you do. The built-in cross MATLAB function will provide the cross product of two vectors, but doing so requires that the vectors be defined in three dimensions. MATLAB is the easiest and most productive computing environment for engineers and scientists. Alternatively, if two segments are parallel, the cross product will be 0 (as A X B = |A|*|B|*sin(theta), and theta of 0 or 180 will return 0), and this will provide a great check for discriminating possibilities 1,2,3 and 4,5. A cross product returns the vector perpendicular to two given vectors.
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In order to determine collinearity and intersections, we will take advantage of the cross product. There are 5 possibilities if we have two line segments:ġ) The two line segments are collinear and overlapping (intersecting portion is a line segment)Ģ) The two line segments are collinear and disjoint (not intersecting)ģ) The two line segments are parallel (not intersecting) While preparing this post, I ran across his response, and I can’t do it much more justice, so here is his general implementation in MATLAB. Note: Much credit for this post and explanation should be given to Gareth Rees.
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Previously, we’ve described how to define a line segment in MATLAB, and we will use this definition in our current method for solving for line intersections. This will allow for further solutions for more complex questions, including a general solution regarding whether a point is inside or outside of a convex or non-convex polygon. One computational geometry question that we will want to address is how to determine the intersection of two line segments.